As the core power unit of new energy vehicles, the accurate modeling of power batteries is of great significance for evaluating their operating status, diagnosing faults throughout their lifecycle, and ensuring safety control under multiple operating conditions. The electrochemical model represented by the P2D model serves as a mechanistic model that can characterize the internal electrochemical reaction process of batteries on a microscale. Its accurate description of the aging and heating behavior of power batteries is an important basis for evaluating the capacity degradation, increase in internal resistance, uneven heating, and inconsistent performance of battery modules. The paper summarizes the latest advances in electrochemical modeling of lithium-ion power batteries, analyzes the coupling methods and application status of electrochemical models with equivalent circuit models, aging models, and thermal models, and focuses on the problem of numerous parameters and difficult identification of electrochemical models. In this paper, the advantages and disadvantages of the single particle model, single particle model with electrolyte, electrochemical mean model, solid-liquid phase reconstruction model, one-dimensional electrochemical model and other methods are compared with each other and analyzed for reducing the order of power battery electrochemical models, the key difficulties in characterizing electrochemical model order reduction are pointed out, and the research trends of electrochemical model reduction order reconstruction methods are prospected, in order to provide direction for the research on electrochemical model reduction order reconstruction of power batteries.